b) Method 1: Expand, Then Factor
\[
(3 x+8)^{2}-(x-2)^{2}
\]

Answer

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Answer

\(\boxed{4(x + 5)(2x + 3)}\) is the final answer.

Steps

Step 1 ：Expand both expressions inside the parentheses: \((3x+8)^{2} = 9x^2 + 48x + 64\) and \((x-2)^{2} = x^2 - 4x + 4\)

Step 2 ：Subtract the second expression from the first one: \(9x^2 + 48x + 64 - (x^2 - 4x + 4) = 8x^2 + 52x + 60\)

Step 3 ：Factor the resulting expression: \(8x^2 + 52x + 60 = 4(x + 5)(2x + 3)\)

Step 4 ：\(\boxed{4(x + 5)(2x + 3)}\) is the final answer.